Receiver Tank Calculator

Detailed Description

This calculator provides four engineering methods for sizing receiver tanks in a compressed air system and a standalone method for computing the usable air capacity of an existing tank. All formulas use U.S. customary units. For symbol consistency, all sizing methods use \(V_{required}\) for the required receiver volume.

A receiver tank (also called an air receiver or storage tank) is a pressure vessel that stores compressed air between the compressor and the distribution system. It serves several purposes:

• Buffers short-duration demand peaks so the compressor does not short-cycle.
• Provides a reserve of compressed air when demand momentarily exceeds supply.
• Dampens pressure pulsations from reciprocating compressors.
• Separates moisture and oil carried over from the compressor.

Choosing the correct tank volume is critical: an undersized tank causes excessive compressor cycling and pressure drops.

The calculation methods are:

1. Usable Capacity – determines the volume of standard cubic feet actually available between two operating pressures for an existing or proposed tank.
2. General – the simplest sizing method; computes the tank volume needed to supply a known air demand within an allowable pressure drop.
3. Dedicated Storage – determines the amount of compressed air storage required to support a short-duration event without causing system pressure to fall below an acceptable minimum. Assumes storage alone supplies the additional air demand during the event, with no significant compressor recovery during the storage discharge period.
4. Metered Storage – used when a compressor can partially replenish the storage volume during the demand event through a controlled recovery flow. The recovery flow is typically regulated by a needle valve that meters air into or out of the storage receiver at a slower fixed rate. Accounts for both the stored air and the metered recovery flow available during the event, often reducing the required storage volume compared to a storage-only design; also computes the tank refill time after the event.
5. Bridging Compressor Reaction Delay – sizes a tank that must supply air during the time the pressure signal propagates from a demand event back to the compressor room and the compressor responds.
6. Compressor Cycle – sizes a tank from the compressor's load/unload duty cycle and the operating pressure band, ensuring the compressor does not short-cycle.

Relevant formulas are documented below.

Usable Air Capacity

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Volume of standard cubic feet of air available between two operating pressures.

The usable capacity is the difference between the air stored at the charging (inlet) pressure and the air remaining at the cut-out (outlet) pressure, expressed in standard cubic feet. The tank volume in gallons is first converted to cubic feet, then scaled by the pressure differential relative to atmospheric pressure.

\begin{equation}\label{eq:receiver-tank-usable-capacity} V_{usable} = \frac{V_{tank}}{k_{gal}} \cdot \frac{P_{in} - P_{out}}{P_{atm}} \end{equation}

Symbols

\(V_{usable}\)	Usable air storage capacity \([\unit{ \scf}]\)
\(V_{tank}\)	Tank volume \([\unit{ \gallon}]\)
\(k_{gal}\)	Gallons per cubic foot (7.48) \([\unit{ \gallon\per\cubicFoot}]\)
\(P_{in}\)	Charging (inlet) pressure \([\unit{ \psi}]\)
\(P_{out}\)	Cut-out (outlet) pressure \([\unit{ \psi}]\)
\(P_{atm}\)	Atmospheric pressure (14.7 psia at sea level) \([\unit{ \psi}]\)

General Method

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Sizes a receiver tank from a known air demand and allowable pressure drop.

The General method assumes the entire air demand must come from stored compressed air. This is the usable-capacity relation solved for required tank size, using the same pressure symbols as the Usable Capacity method.

\begin{equation}\label{eq:receiver-tank-general-size} V_{required} = V_{usable} \cdot \frac{P_{atm}}{P_{in} - P_{out}} \cdot k_{gal} \end{equation}

Equivalent form: \(V_{required} = Q_{demand} \cdot \frac{P_{atm}}{\Delta P} \cdot k_{gal}\), where \(Q_{demand} = V_{usable}\) and \(\Delta P = P_{in} - P_{out}\).

Symbols

\(V_{required}\)	Required receiver tank size \([\unit{ \gallon}]\)
\(V_{usable}\)	Required usable air drawn from the tank \([\unit{ \cubicFoot}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)
\(P_{in}\)	Initial tank pressure for drawdown \([\unit{ \psi}]\)
\(P_{out}\)	Final tank pressure for drawdown \([\unit{ \psi}]\)
\(\Delta P\)	Pressure drop, \(P_{in} - P_{out}\) \([\unit{ \psi}]\)
\(k_{gal}\)	Gallons per cubic foot (7.48) \([\unit{ \gallon\per\cubicFoot}]\)

Dedicated Storage Method

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Determines the compressed air storage volume needed to support a short-duration demand event without letting system pressure fall below an acceptable minimum.

Use this method when storage alone must supply the additional air demand during the event, with no significant compressor recovery occurring during the storage discharge period. The tank is sized so that pressure can fall from the initial stored value to the minimum acceptable value while satisfying the full demand flow rate for the duration of the event.

\begin{equation}\label{eq:receiver-tank-dedicated-storage-size} V_{required} = \frac{k_{gal} \cdot t_{demand} \cdot Q_{flow} \cdot P_{atm}}{P_{in} - P_{out}} \end{equation}

Symbols

\(V_{required}\)	Required receiver tank size \([\unit{ \gallon}]\)
\(k_{gal}\)	Gallons per cubic foot (7.48) \([\unit{ \gallon\per\cubicFoot}]\)
\(t_{demand}\)	Duration of the air demand event \([\unit{ \minute}]\)
\(Q_{flow}\)	Required air flow rate during the demand event \([\unit{ \cubicFoot\per\minute}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)
\(P_{in}\)	Initial tank pressure \([\unit{ \psi}]\)
\(P_{out}\)	Final tank pressure \([\unit{ \psi}]\)

Metered Storage Method — Tank Size

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Sizes a dedicated storage tank when the compressor can partially replenish storage during the demand event through a controlled recovery flow.

Use this method when a compressor can partially replenish the storage volume during the demand event through a controlled recovery flow. In many compressed air systems this recovery flow is regulated by a needle valve that meters air into or out of the storage receiver at a slower fixed rate \(Q_{metered}\). The calculator accounts for both the stored air and the metered recovery flow available during the event: only the net demand \((Q_{flow} - Q_{metered})\) draws from the stored volume, often reducing the required tank size compared to a storage-only design. This method is appropriate for intermittent, high-flow applications where a controlled refill rate is desired.

\begin{equation}\label{eq:receiver-tank-metered-storage-size} V_{required} = \frac{k_{gal} \cdot t_{demand} \cdot (Q_{flow} - Q_{metered}) \cdot P_{atm}}{P_{in} - P_{out}} \end{equation}

Symbols

\(V_{required}\)	Required receiver tank size \([\unit{ \gallon}]\)
\(k_{gal}\)	Gallons per cubic foot (7.48) \([\unit{ \gallon\per\cubicFoot}]\)
\(t_{demand}\)	Duration of the air demand event \([\unit{ \minute}]\)
\(Q_{flow}\)	Required air flow rate during the demand event \([\unit{ \cubicFoot\per\minute}]\)
\(Q_{metered}\)	Metering valve (needle valve) flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)
\(P_{in}\)	Initial tank pressure \([\unit{ \psi}]\)
\(P_{out}\)	Final tank pressure \([\unit{ \psi}]\)

Metered Storage Method — Refill Time

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Time required to refill the receiver tank after a metered storage demand event.

After a demand event empties the tank from \(P_{in}\) to \(P_{out}\), the metering valve continues to supply air at \(Q_{metered}\) while the system pressure recovers. The refill time is the time required to re-pressurize the tank volume \(V_{cf}\) from \(P_{out}\) back to \(P_{in}\) at the constant metered flow rate. The intermediate computation yields a time in minutes (since \(Q_{metered}\) is in cfm); multiplying by 60 converts to seconds.

\begin{equation}\label{eq:receiver-tank-metered-storage-refill} T_{refill} = \frac{60 \cdot V_{cf} \cdot (P_{in} - P_{out})}{Q_{metered} \cdot P_{atm}} \end{equation}

where \(V_{cf} = V_{required} \cdot k_{cf}\) is the tank volume in cubic feet.

Symbols

\(T_{refill}\)	Tank refill time \([\unit{ \second}]\)
\(60\)	Seconds per minute conversion \([\unit{ \second\per\minute}]\)
\(V_{cf}\)	Tank volume in cubic feet \([\unit{ \cubicFoot}]\)
\(k_{cf}\)	Cubic feet per gallon (0.133681) \([\unit{ \cubicFoot\per\gallon}]\)
\(V_{required}\)	Required receiver tank size \([\unit{ \gallon}]\)
\(P_{in}\)	Initial tank pressure \([\unit{ \psi}]\)
\(P_{out}\)	Final tank pressure \([\unit{ \psi}]\)
\(Q_{metered}\)	Metering valve flow rate \([\unit{ \cubicFoot\per\minute}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)

Bridging Compressor Reaction Delay Method

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Sizes a tank to bridge the compressor reaction delay for a remote demand event.

When a sudden air demand occurs at a point distant from the compressor room, the pressure drop signal must travel back through the distribution piping to the compressor before the compressor can respond. During this transit time \(t_{transit} = d_{pipe} / v_{air}\) (in seconds), the receiver must supply all the required air. The formula converts the transit time to an equivalent tank volume using the air demand flow rate, pressure ratio, and the gallon-to-cubic-foot conversion.

\begin{equation}\label{eq:receiver-tank-bridging-size} V_{required} = \frac{d_{pipe}}{v_{air}} \cdot \frac{Q_{demand}}{60} \cdot \frac{P_{atm}}{\Delta P} \cdot k_{gal} \end{equation}

Symbols

\(V_{required}\)	Required receiver tank size \([\unit{ \gallon}]\)
\(d_{pipe}\)	Distance from demand event to compressor room \([\unit{ \foot}]\)
\(v_{air}\)	Speed of compressed air in distribution piping \([\unit{ \foot\per\second}]\)
\(Q_{demand}\)	Air demand at the event location \([\unit{ \cubicFoot\per\minute}]\)
\(60\)	Seconds per minute conversion \([\unit{ \second\per\minute}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)
\(\Delta P\)	Allowable pressure drop at the demand event \([\unit{ \psi}]\)
\(k_{gal}\)	Gallons per cubic foot (7.48) \([\unit{ \gallon\per\cubicFoot}]\)

Note

The factor \(d_{pipe} / v_{air}\) yields the signal transit time in seconds. Dividing \(Q_{demand}\) by 60 converts from cfm to ft³/s so the product of transit time × flow rate gives a volume in ft³, which is then scaled to gallons.

Compressor Cycle Method

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Sizes a receiver tank from the compressor duty cycle and operating pressure band.

The Compressor Cycle method derives the required storage volume directly from the compressor's load/unload pattern. The effective net capacity is the fraction of the compressor's rated output consumed over a full cycle; the tank must store the air that accumulates during the unloaded phase so that system pressure stays within \(P_{load}\) to \(P_{unload}\).

\begin{equation}\label{eq:receiver-tank-compressor-cycle-size} V_{required} = \frac{Q_{comp} \cdot t_{load} \cdot t_{unload} \cdot P_{atm}} {60 \cdot (t_{load} + t_{unload}) \cdot (P_{unload} - P_{load})} \cdot k_{gal} \end{equation}

Derivation

The effective net capacity consumed per unit time is:

\begin{equation}\label{eq:receiver-tank-compressor-cycle-capacity} Q_{eff} = \frac{t_{load}}{t_{load} + t_{unload}} \cdot Q_{comp} \end{equation}

The volume (ft³) that must be stored during the unloaded phase is:

\begin{equation}\label{eq:receiver-tank-compressor-cycle-vcf} V_{cf} = \frac{Q_{eff} \cdot t_{unload} / 60}{(P_{unload} - P_{load}) / P_{atm}} \end{equation}

Converting to gallons gives \(V_{required} = V_{cf} \cdot k_{gal}\).

Symbols

\(V_{required}\)	Required receiver tank size (liquid storage volume) \([\unit{ \gallon}]\)
\(V_{cf}\)	Required storage volume (area storage volume) \([\unit{ \cubicFoot}]\)
\(Q_{comp}\)	Rated compressor capacity at full load \([\unit{ \cubicFoot\per\minute}]\)
\(Q_{eff}\)	Effective net capacity consumed per cycle \([\unit{ \cubicFoot\per\minute}]\)
\(\Delta P\)	Pressure band width ( \(P_{unload} - P_{load}\)) \([\unit{ \psi}]\)
\(t_{load}\)	Compressor loaded time per cycle \([\unit{ \minute}]\)
\(t_{unload}\)	Compressor unloaded time per cycle \([\unit{ \minute}]\)
\(P_{atm}\)	Atmospheric pressure \([\unit{ \psi}]\)
\(P_{unload}\)	Compressor unload (cut-out) pressure \([\unit{ \psi}]\)
\(P_{load}\)	Compressor full-load (cut-in) pressure \([\unit{ \psi}]\)
\(60\)	Seconds per minute conversion \([\unit{ \second\per\minute}]\)
\(k_{gal}\)	Gallons per cubic foot (7.48) \([\unit{ \gallon\per\cubicFoot}]\)

Returned intermediate results

In addition to \(V_{required}\), the calculation returns:

• effectiveCapacity ( \(Q_{eff}\)) — average flow delivered over a full cycle \([\unit{\cubicFoot\per\minute}]\)
• pressureChange ( \(\Delta P\)) — operating pressure band width \([\unit{\psi}]\)
• volumeCf ( \(V_{cf}\)) — required area storage volume before gallon conversion \([\unit{\cubicFoot}]\)

Modules
	Usable Air Capacity Formula
	Volume of standard cubic feet of air available between two operating pressures.
	General Method Tank Size Formula
	Sizes a receiver tank from a known air demand and allowable pressure drop.
	Dedicated Storage Method Tank Size Formula
	Determines the compressed air storage volume needed to support a short-duration demand event without letting system pressure fall below an acceptable minimum.
	Metered Storage Method Tank Size Formula
	Sizes a dedicated storage tank when the compressor can partially replenish storage during the demand event through a controlled recovery flow.
	Metered Storage Method Refill Time Formula
	Time required to refill the receiver tank after a metered storage demand event.
	Bridging Compressor Reaction Delay Method Formula
	Sizes a tank to bridge the compressor reaction delay for a remote demand event.
	Compressor Cycle Method Tank Size Formula
	Sizes a receiver tank from the compressor duty cycle and operating pressure band.

Files
file	receiver_tank.h
	Declarations for compressed air receiver tank sizing and capacity calculations.

Namespaces
namespace	receiver_tank
	Compressed air receiver tank sizing and usable capacity calculations.

Classes
struct	receiver_tank::UsableCapacityInput
	Input parameters for the usable air capacity calculation. More...
struct	receiver_tank::UsableCapacityResult
	Result of the usable air capacity calculation. More...
struct	receiver_tank::GeneralInput
	Input parameters for the General sizing method. More...
struct	receiver_tank::SizeResult
	Tank size result shared by the General, Dedicated Storage, and Bridging methods. More...
struct	receiver_tank::DedicatedStorageInput
	Input parameters for the Dedicated Storage sizing method. More...
struct	receiver_tank::MeteredStorageInput
	Input parameters for the Metered Storage sizing method. More...
struct	receiver_tank::MeteredStorageResult
	Result of the Metered Storage sizing calculation. More...
struct	receiver_tank::BridgingInput
	Input parameters for the Bridging Compressor Reaction Delay sizing method. More...
struct	receiver_tank::CompressorCycleInput
	Input parameters for the Compressor Cycle sizing method. More...
struct	receiver_tank::CompressorCycleResult
	Result of the Compressor Cycle sizing calculation. More...